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If X is a 3-digit number, is it odd? (1) X is a perfect square.

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If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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New post Updated on: 23 Sep 2018, 02:24
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If X is a 3-digit number, is it odd?

(1) X is a perfect square.
(2) X is a palindrome.
Spoiler: OA

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Originally posted by aa008 on 22 Sep 2018, 23:36.
Last edited by Bunuel on 23 Sep 2018, 02:24, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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New post Updated on: 23 Sep 2018, 01:40
aa008 wrote:
If X is a 3- digit number, is it odd?

1). X is a perfect square.
2). X is a palindrome.


OA: E
1). X is a perfect square.
X can be \(121,144,169...\) and so on.
Unit digit of X can be even or odd
Statement 1 alone is not sufficient.

2). X is a palindrome.
X can be \(121,131,141,.....212,222\) and so on.
Unit digit of X can be even or odd
Statement 2 alone is not sufficient.

Combining \((1)\) and \((2)\),X should be a perfect square and a palindrome.
X can be \(121(11^2), 484(22^2)\) as there is no unique value of X and unit digit of X can be even or odd, Combining (1) and (2) will also be insufficient.

Originally posted by Bismarck on 23 Sep 2018, 01:28.
Last edited by Bismarck on 23 Sep 2018, 01:40, edited 1 time in total.
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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New post 23 Sep 2018, 01:35

Solution



Given:
    • X is a 3-digit number

To find:
    • Whether X is odd or not.

Analysing Statement 1
As per the information given in statement 1, X is a perfect square.
    • Starting from 100 to 961, we have many even and odd perfect squares

Therefore, statement 1 is not sufficient

Analysing Statement 2
As per the information given in statement 2, X is palindrome.
    • In 3-digits, we have many even as well as odd numbers which are palindromes.

Therefore, statement 2 is not sufficient.

Combining Both Statements
We know, X is a 3-digit perfect square, which is also a palindrome.
Possible values of X can be
    • \(11^2 = 121\)
    • \(22^2 = 484\)
    • \(26^2 = 676\)

As we can see, X can be both even or odd.

Hence, the correct answer is option E.
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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New post 29 Sep 2018, 00:08
1. X can be 121,144 etc. It can be even or odd. Hence insufficient
2. X can be 121,212 etc. It can be even or odd. Hence insufficient
Combining both statements X can be 121 or 484.
Hence answer is E
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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New post 19 Sep 2019, 08:47
aa008 wrote:
If X is a 3-digit number, is it odd?

(1) X is a perfect square.
(2) X is a palindrome.


100≤X≤999

(1) X is a perfect square: X={121,144,169,196…}; insufic.
(2) X is a palindrome: X={121,222,313,505,808…}; insufic.
(1&2) X=perfect square-palindrome={11^2,(2*11)^2…}={121,484,…}; insufic.

Answer (E)
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.   [#permalink] 19 Sep 2019, 08:47
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